After a few seconds the door could be closed again. You can tell by a slight difference in how wide open it is. That one looks like it could be closed.
But yeah being stuck in a deathtrap room sucks. Worst is when your medbay gets hacked. Usually certain death for anyone inside.
And that is the reason why I never keep anyone in my medibay.
And yes, breached doors repair after a while, if you have a powerful enough oxygen system (I think 2 bars but it might take 3) You can keep even vaccumed rooms as oxygenized enough so that no damage takes place. (Your ships total oxygen will not increase but will stay constant.) Just make sure you open the doors to other rooms for them to vent.
Also the FLAK 2 is a must have item if you plan on getting anywhere, it completely stuffs on shield systems and basically gives you an opening to rape enemy ships.
Also if your door control has at least one bar you will be able to control doors, even if a door is smashed open it will eventually heal itself.
Again though, hacking hardware is your friend, top priority hardware to have because it can stop most anything from stuffting on your ship in annoying bullstuff ways. (Infact, if the enemy using an Anti-drone EMP defensive drone, this will only temporarily disable your hacking drone, it can still reacquire power and hit the targeted system after a minute or so.)
I'll be honest here though, despite my heavy veterancy with this game (everything unlocked, beaten the game once with each ship design.) I have yet to survive an instance where one of those breach ion drones hits my ship and wrecks everything. I've only encountered them twice however, but they still destroy me each time. I'm assuming this is what anti-drones are for, as well as the defensive drone for your ship's interior; but oh lord these stupid buggers are annoying.